List of top Questions asked in PSEB XII

If \( P(A) = \frac{1}{2}, P(B) = \frac{3}{8} \) and \( P(A \cap B) = \frac{1}{5} \), then \( P(A|B) \) is equal to:
Ram and Rahim are contesting for two vacancies in a company. Probability of selection of Ram is \( \frac{7}{9} \) and that of Rahim is \( \frac{4}{7} \). What is the probability that both will be selected?
Find \( \frac{d}{dx}(x^x) \) and evaluate whether this result is true \( \forall x \in \mathbb{R} \).
Evaluate \( \int \frac{2x-3}{x^2+1} dx \).
Using integration, find the area bounded by the circle whose centre is at origin and radius is 4 units.
The volume of spherical balloon is increasing at the rate of 25 c.c./s. Find the rate of change of its surface area at the instant when its radius is 5cm.
Order of differential equation \( \frac{d^2y}{dx^2} - 2\frac{dy}{dx} + 3y = 0 \) is:
If \( \vec{a} \) is a non-zero vector then \( |\vec{a} \times \vec{a}| \) is equal to:
Name of the inequality \( |\vec{a} \cdot \vec{b}| \le |\vec{a}| |\vec{b}| \) is:
Direction ratios of the straight line \( \vec{r} = 2\hat{i} - 3\hat{j} + \hat{k} + m(9\hat{i} - 2\hat{j} + 5\hat{k}) \) are:
Vector equation of the line \( \frac{x-5}{-4} = \frac{y-3}{5} = \frac{z+3}{-8} \) is:
Objective function of a linear programming problem is:
If \( y = e^{\log x} \), then \( \frac{dy}{dx} \) is:
If \( y = \tan x \), then at \( x = \frac{\pi}{4} \), \( \frac{dy}{dx} \) is equal to:
Radius of a circle is increasing at the rate of \( 2 \text{ m/s} \). Rate of change of its circumference is:
\( \int_{\pi/6}^{\pi/3} \frac{\sqrt{\cos x}}{\sqrt{\sin x} + \sqrt{\cos x}} dx \) is equal to:
\( \int_0^1 \frac{dx}{1+x^2} \) is equal to:
Range of function \( \cos^{-1} x \) is:
Principal value of \( \sin^{-1}(1) \) is:
If \( A \) is a square matrix of order \( 2 \times 2 \) and \( |A| = 5 \), then \( |Adj(A)| \) is:
If the order of the matrix \( A \) is \( 3 \times 2 \), then the order of the matrix \( (A')' \) is:
State Gauss’s theorem. Using this theorem, derive electric field intensity due to thin uniformly charged infinite plane sheet.
Define capacitance. Derive capacitance of a parallel plate capacitor having dielectric slab between its plates.
With help of labelled diagram, write principle of astronomical telescope and derive expression for magnifying power of an astronomical telescope, when final image is formed at least distance of distinct vision.
What is interference of light? Derive an expression for the fringe width in the Young’s double slit experiment.